Fluid Mechanics Viscosity Question 147
Question: The flow of blood in a large artery of a anesthetized dog is diverted through a venturimeter. The wider part of the meter has cross-sectional area equal to that of the artery, i.e.,$ 10mm^{2} $ . The narrower part has an area$ 5mm^{2} $ . The pressure drop in the artery is 22 Pa. Density of the blood is$ 1.06\times 10^{3}kg{{m}^{-3}} $ . The speed of the blood in the artery is
Options:
A) $ 0.12,m,{{s}^{-1}} $
B) $ 0.62,m,{{s}^{-1}} $
C) $ 0.24,m,{{s}^{-1}} $
D) $ 0.42,m,{{s}^{-1}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Here,$ A=10mm^{2},a=5mm^{2},\rho =1.06\times 10^{2}kg{{m}^{-3}} $ $ =1060kg{{m}^{-3}},p_{1}-p_{2}=22pa $ Speed of the fluid through the wide neck is $ v=\sqrt{\frac{2(P_{1}-P_{2})}{\rho }}{{\left{ {{\left( \frac{A}{a} \right)}^{2}}-1 \right}}^{-1/2}} $ Or $ \frac{A}{a}=\frac{10}{5}=2 $ $ \therefore v=\sqrt{\frac{2\times 22}{1060(2^{2}-1)}}=0.12m{{s}^{-1}} $
BETA
